Void Inclusions Research Articles

Elastic properties of woven bone: effect of mineral content and collagen fibrils orientation.

Woven bone is a type of tissue that forms mainly during fracture healing or fetal bone development. Its microstructure can be modeled as a composite with a matrix of mineral (hydroxyapatite) and inclusions of collagen fibrils with a more or less random orientation. In the present study, its elastic properties were estimated as a function of composition (degree of mineralization) and fibril orientation. A self-consistent homogenization scheme considering randomness of inclusions' orientation was used for this purpose. Lacuno-canalicular porosity in the form of periodically distributed void inclusions was also considered. Assuming collagen fibrils to be uniformly oriented in all directions led to an isotropic tissue with a Young's modulus [Formula: see text]GPa, which is of the same order of magnitude as that of woven bone in fracture calluses. By contrast, assuming fibrils to have a preferential orientation resulted in a Young's modulus in the preferential direction of 9-16GPa depending on the mineral content of the tissue. These results are consistent with experimental evidence for woven bone in foetuses, where collagen fibrils are aligned to a certain extent.

Optimizing the layout of discrete objects in structures and materials: A projection-based topology optimization approach

This paper uses topology optimization to optimize the layout of discrete objects, such as fixed-shape void, stiffening, or functional inclusions, in structures and periodic materials. The methodology follows a material distribution approach and the Heaviside Projection Method (HPM) is manipulated to ensure that the designed objects are discrete, of fixed size (length scale) and shape, and satisfy minimum spacing requirements. These restrictions are achieved implicitly through projection without additional constraints or heuristics. The methodology is built in the spirit of free-form topology optimization and thus discrete objects are shown to appear, vanish, or translate across the design domain during the design evolution. The technique is demonstrated on problems governed by mechanical stiffness including the design of structures and material microstructures whose elastic stiffness is to be enhanced by optimizing the location of stiff, circular inclusions.

A micromechanical model for concrete under static loading

A micromechanical model is developed to describe the stress–strain behaviours of concrete under uniaxial compression. Two kinds of defects are considered, namely microcracks around the mortar–coarse aggregate interface or the interfacial transition zone and aligned coalesced cracks in the concrete. The mortar–coarse aggregate interfaces (interfacial transition zone) are modelled as spring layers between the mortar matrix and the inclusions (aggregates) and the existences of the microcracks in the interfacial transition zone are considered as reductions of the spring parameters under the frame of the Mori–Tanaka method. The aligned coalesced cracks in concrete (mortar + aggregate) are treated as void inclusions in the matrix of concrete using the Mori–Tanaka scheme as well. Stochastic evolution rules are adopted for both defects. The numerical examples are worked out and the proposed model is shown to be capable of estimating the moduli of concrete under its whole loading process.

Simulation study of the impact of interface roughness and void inclusions on Cu(In,Ga)(Se,S)2 solar cells

Typical features of sequentially processed Cu(In1−xGax)(Sey−1Sy)2 (CIGSSe) thin film solar cells such as roughness at particular interfaces and free absorber volume (voids) might influence the device characteristics significantly. We investigated the influence of both, roughness and voids, on the solar cell performance parameters as well as on the device capacitance by means of two-dimensional (2D) device simulations. Increased roughness was found to enhance light absorption and carrier collection whereas the increased interface recombination at the textured heterojunction is of minor relevance compared to the performance gain. However, the enlarged interface area must be taken into account when considering measurements of the device capacitance. Void inclusions in the rear section of the absorber support infrared absorption because of internal reflection. This leads to slight improvement of the device performance unless the back contact coverage does not come below 30%. Additionally, voids appear to be less critical in terms of surface recombination at the void/CIGSSe interface given that increased gallium concentration is present.

Non-uniform capillary model for unidirectional fiber bundles considering pore size distribution

Capillary rise affects void inclusion during the impregnation of fiber reinforcements in resin transfer molding. A new model of effective capillary radius has been developed to investigate the effect of pore size distribution on capillary flow in unidirectional fiber bundles. With the image analysis method, the statistical results showed that the pore size distribution could be very different even for the same fiber volume fraction. Then, the classical Washburn equation, in conjunction with different models for calculating effective capillary radius, was applied to predict the capillary rise rate. Compared with the experimental results, we found that the new model performed better than traditional models where the effective capillary radius was obtained using average pore radius or hydraulic radius.

Macroscopic effective mechanical properties of porous dry concrete

Abstract The pores and voids within concrete have a great influence on the macroscopic elastic modulus, strength and other mechanical properties of concrete. The present study determines the macroscopic mechanical properties of porous dry concrete composed of hollow void inclusions embedded in a concrete matrix. Based on a three-phase sphere model, the effective bulk modulus of a concrete composite with a hollow sphere in concrete matrix is obtained. The investigation on the influence of porosity on the effective shear modulus of porous dry concrete is carried out by using a hollow cylindrical tube model. Based on the assumption that the material is isotropic, homogeneous and elastic, the effective Young's modulus and Poisson's ratio of porous concrete composites are derived. A comparison between the elastic modulus and Poisson's ratio derived from the present model and those from open literature indicates a good agreement. Furthermore, on the basis of the developed simplified analytical model, the quantitative effect of porosity on the macroscopic effective tensile and shear strengths of porous concrete in dry state are studied. Besides, their corresponding effective peak strains when porous dry concrete reaches its macroscopic effective tensile/shear strengths are also investigated and discussed. Also a comparison between the available tensile strength and two classical solutions is made to verify the rationality and accuracy of the present approach. The consistent results indicate that the proposed approach can predict the effective mechanical properties of porous dry concrete well, and the formulas are simple and convenient to use.

Generalized self-consistent scheme for the effective behavior of viscoelastic heterogeneous media: A simple approximate solution

This paper gives a simple approximate solution for obtaining the effective behavior of linear viscoelastic heterogeneous media for the case of elastic inclusions immersed within a viscoelastic matrix. The solution in the Laplace–Carson space is obtained by the Generalized self-consistent model and the simplification is in an explicit expression of the inverse Laplace transform. It is shown that the solution in Laplace–Carson space can be approximated by a convenient rational fraction which is given explicitly as a function of viscoelastic parameters. This provides an easy way to perform the inverse Laplace transform. Examples of typical composites, including possibly void and rigid inclusions, are provided and show that the procedure provides reasonably accurate results. In addition, a complete rheological representation can be provided in some cases for describing the behavior of the effective medium.

ELASTIC PROPERTIES OF WOVEN BONE: EFFECT OF MINERAL CONTENT AND COLLAGEN FIBRILS ORIENTATION

Woven bone is a type of tissue that forms mainly during fracture healing or fetal bone development. Its microstructure can be modeled as a composite with a matrix of mineral (hydroxyapatite) and inclusions of collagen fibrils with a more or less random orientation. In the present study, its elastic properties were estimated as a function of composition (degree of mineralization) and fibril orientation. A self-consistent homogenization scheme considering randomness of inclusions’ orientation was used for this purpose. Lacuno-canalicular porosity in the form of periodically distributed void inclusions was also considered. Assuming collagen fibrils to be uniformly oriented in all directions led to an isotropic tissue with a Young’s modulus \(E = 1.90\) GPa, which is of the same order of magnitude as that of woven bone in fracture calluses. By contrast, assuming fibrils to have a preferential orientation resulted in a Young’s modulus in the preferential direction of 9–16 GPa depending on the mineral content of the tissue. These results are consistent with experimental evidence for woven bone in foetuses, where collagen fibrils are aligned to a certain extent.

Vibro-acoustic response of an infinite, rib-stiffened, thick-plate assembly using finite-element analysis

The vibration of and sound radiation from an infinite, fluid-loaded, thick-plate assembly stiffened periodically with ribs are investigated numerically using finite-element analysis. First, numerical simulations are compared to the analytical solutions presented recently for this particular problem [Hull and Welch, J. Sound Vib. 329, 4192-4211 (2010)]. It is shown that the solutions reported in this reference are partially incorrect because the number of modes was not chosen correctly. Subsequently, the numerical model is used to study the effect of repeated and equally spaced void inclusions on the vibro-acoustic response of the system.

The Influence of Processing Parameters on the Void Content and Compressive Strength of Carbon Fibre-Epoxy Laminates

This research addresses the influence of various processing parameters on the post cure quality of carbon fibre composites. Four processing parameters were investigated in the study, in terms of their impact on void content and overall compressive strength. The first parameter distinguishes between laminates cured in a vacuum oven and those cured in an autoclave under high positive pressure. The second parameter describes the impact on voids of differing fibre architectures, comparing a unidirectional fibre structure to that of woven cloth. Thirdly, the influence of compaction during manufacture is analysed and lastly, variation in cure temperature was tested to determine its effect on final laminate quality. The quality of the cured laminate samples was assessed from visual inspection, and in terms of compressive strength and void fraction calculated by Micro-CT X-ray Tomography. The results show that autoclave-cured samples feature significant quality improvements in terms of void fraction and compressive strength when compared to oven-cured samples. Unidirectional laminates incur higher sensitivity to void inclusion than cloth laminates due to the influence of fibre wrinkling. Compaction has no effect on laminate strength; it does however reduce variability in certain cases. Temperature affects different fibre structures in different ways, these being highly dependent on curing method. Finally, it was discerned that curing by autoclave was the dominant processing parameter. Thus, regardless of other manufacturing techniques, the autoclave samples featured almost zero voids and were consequently of the highest quality.

The M-Integral Analysis for a Nano-Inclusion in Plane Elastic Materials Under Uni-Axial or Bi-Axial Loadings

This paper deals with the M-integral analysis for a nano-inclusion in plane elastic materials under uni-axial or bi-axial loadings. Based on previous works (Gurtin and Murdoch, 1975, “A Continuum Theory of Elastic Material Surfaces,” Arch. Ration. Mech. Anal., 57, pp. 291–323; Mogilevskaya, et al., 2008, “Multiple Interacting Circular Nano-Inhomogeneities With Surface/Interface Effects,” J. Mech. Phys. Solids, 56, pp. 2298–2327), the surface effect induced from the surface tension and the surface Lamé constants is taken into account, and an analytical solution is obtained. Four kinds of inclusions including soft inclusion, hard inclusion, void, and rigid inclusions are considered. The variable tendencies of the M-integral for each of four nano-inclusions against the loading or against the inclusion radius are plotted and discussed in detail. It is found that in nanoscale the surface parameters for the hard inclusion or rigid inclusion have a little or little influence on the M-integral, and the values of the M-integral are always negative as they would be in macroscale, whereas the surface parameters for the soft inclusion or void yield significant influence on the M-integral and the values of the M-integral could be either positive or negative depending on the loading levels and the surface parameters. Of great interest is that there is a neutral loading point for the soft inclusion or void, at which the M-integral transforms from a negative value to a positive value, and that the bi-axial loading yields similar variable tendencies of the M-integral as those under the uni-axial tension loading. Moreover, the bi-axial tension loading increases the neutral loading point, whereas the bi-axial tension-compression loading decreases it. Particularly, the magnitude of the negative M-integral representing the energy absorbing of the soft inclusion or void increases very sharply as the radius of the soft inclusion or void decreases from 5 nm to 1 nm.

Thermal and Electroelastic Behavior of Piezocomposites and Inhomogeneous Piezoelectric Materials with Voids

This article presents an incremental self-consistent model that is used to optimize two kinds of thermoelectroelastic composites: polymer/ceramic and ceramic/void. The modeling is based on the heterogeneous inclusion problem of Eshelby, which leads to an expression for the strain−electric field relation by integral equations. The solution of these equations leads to expressions for electroelastic concentration tensors based on a micromechanical model. The overall thermal and electroelastic behavior of the composites considered can be estimated by means of these concentration tensors. An incremental self-consistent scheme is introduced that improves upon the classical self-consistent model for piezoelectric composites. Predictions using this scheme are compared to predictions based on the Mori−Tanaka and self-consistent models of the thermal and electroelastic behavior of inhomogeneous piezoelectric materials with and without void inclusions. The effects of poling direction and inclusion shape are discussed.

A computational study on the effective properties of heterogeneous random media containing particulate inclusions

The effective elastic modulus and conductivity of a two-phase material system are investigated computationally using a Monte Carlo scheme. The models contain circular, spherical or ellipsoidal inclusions that are either uniformly or randomly embedded in the matrix material. The computed results are compared with the applicable effective medium theories. It is found that the random distribution, geometric permeability and particle aspect ratio have non-negligible effects on the effective material properties. For spherical inclusions, the effective medium approximations agree well with the simulation results in general, but the analytical predictions on void or non-spherical inclusions are much less reliable. It is found that the results for overlapping and non-overlapping inclusions do not differ very much at the same volume fraction. The effect of particle morphology is also investigated by modelling prolate and oblate ellipsoidal inclusions.

A constitutive model for drying of a partially saturated porous material

A new constitutive model for drying of an elastic porous material is presented. The model is derived by decomposing the boundary value problem of drying into parts for which an explicit solution is readily available. The mathematical form differs from models developed using either the concept of equivalent pore pressure or average pore pressure. Instead of pressure averaging, the extent of weakening of the solid due to void inclusions, a material parameter, is found to be critical for the proper predictions of the volumetric strains. The model is applicable to drying under conditions where multi-layer adsorption of liquid persists, i.e. where the effects of solid surface energy are negligible, and where capillary pressure is the primary loading stimulus. A particular (and simple) form of the model is compared with experimental data for partially dried cement paste and Vycor™ glass, and is shown to provide a much better agreement than previous models based on average pore pressure. Implications to the poromechanics and the effective stress of partially saturated porous media are discussed.

Extended Effective-Mean-Field Analysis for Electrical Conductivity of Lotus-Type Porous Nickel

We studied the effective electrical conductivity of lotus-type porous nickel with cylindrical elongated pores by applying the extended effective-mean-field (extended EMF) theory that is based on Hatta-Taya’s theory and Bruggeman’s effective-medium approximation. We modeled lotus-type porous nickel as the composite materials with ellipsoidal void inclusion, and examined the effect of shape and orientation of the pores and applied-electric-field direction on the effective electrical conductivity. The extended EMF theory revealed that well-known Archie’s power law is quite useful for expressing the porosity dependence of the electrical conductivity of lotus-type porous metals even though the deviation of porous morphology exists.

Full band gap for surface acoustic waves in a piezoelectric phononic crystal

A plane-wave-expansion method suited to the analysis of surface-acoustic-wave propagation in two-dimensional piezoelectric phononic crystals is described. The surface modes of a square-lattice Y-cut lithium niobate phononic crystal with circular void inclusions with a filling fraction of 63% are identified. It is found that a large full band gap with a fractional bandwidth of 34% exists for surface acoustic waves of any polarization and incidence, coincidentally with the full band gap for bulk waves propagating in the plane of the surface. The excitation of surface acoustic waves by interdigital transducers is discussed.

Effects of gelatin on mechanical properties of hydroxyapatite-gelatin nano-composites

AbstractA biomimetic reactor has been developed to synthesize hydroxyapatite-gelatin (HAP-GEL) nanocomposites that mimic ultra-structures of natural bone. We hypothesize that in the reactor, gelatin concentration controls morphology and packing structures of HAP crystals. To test the hypothesis, three types of mechanical tests were conducted, including nanoindentation, compression, and fracture tests. Nanoindentation tests in conjunction with computer modeling were used to assess effects on gelatin-induced microstructures of HAP. The results showed that increasing gelatin content increased both the plane strain modulus and the fracture toughness. The gelatin appeared to shorten the HAP crystal distance, which consolidated the internal structure of the composite and made the material more rigid. The fracture toughness KIC increased partially due to the effect of fiber bridging between gelatin molecules. The highest fracture toughness (1.12 MPa·m1/2) was equivalent to that of pure hydroxyapatite. The compressive strength of the HAP-GEL (107.7±6.8 MPa) was, however, less sensitive to microstructural changes and was within the range of natural cortical bone (human 170 MPa, pig: 100 MPa). The compression strength was dominated by void inclusions while the nanoindentation response reflected ultra-structural arrangement of the crystals. The gelatin concentration is likely to modify crystal arrangement as demonstrated in TEM experiments but not void distribution at macroscopic levels.

Boundary effects in Cherenkov radiation

The effect of dielectric boundaries on the Cherenkov radiation (CR) produced when a fast point charge moves inside or near a material is analyzed for different shapes of the sample. Calculations are offered for a charge moving near both planar and nonplanar surfaces. CR is found to be produced even when the external charge moves outside a semi-infinite medium. For charges moving near planar boundaries, the reflected radiation interferes with the direct CR, leading to oscillations in the emission probability as a function of the impact parameter relative to the interfaces. Thin-film guided modes are excited by penetrating electrons and our calculations agree reasonably well with available experiments. The bulk limit in the emission probability is recovered for charges passing by the center of cylinders or spheres of increasingly large radius. Recent experiments of energy loss of electrons passing near dielectric spheres are explained thanks to the inclusion of retardation effects in the sphere response. These effects lead to an efficient channel of radiative energy losses. Finally, the diffraction of CR in void inclusions is proposed as a tool for providing information on otherwise inaccessible buried structures.

Numerical modelling of void inclusions in porous media

AbstractNumerical modelling of porous flow in a low‐permeability matrix with high‐permeability inclusions is a challenging task because the large ratio of permeabilities ill‐conditions the finite element system of equations. We propose a coupled model where Darcy flow is used for the porous matrix and potential flow is used for the inclusions. We discuss appropriate interface conditions in detail and show that the head drop in the inclusions can be prescribed in a very simple way. Algorithmic aspects are treated in full detail. Numerical examples show that this coupled approach precludes ill‐conditioning and is more efficient than heterogeneous Darcy flow. Copyright © 2003 John Wiley & Sons, Ltd.

Circular inclusions in anti-plane strain couple stress elasticity

The solution for a circular inclusion with a prescribed anti-plane eigenstrain is derived. It is shown that the components of the Eshelby tensor within the inclusion, corresponding to a uniform eigenstrain, can be either uniform or non-uniform, depending on the imposed interface conditions. The stress amplification factors due to circular void or rigid inclusion in an infinite medium under remote anti-plane shear stress are calculated. The failure of the couple stress elasticity to reproduce the classical elasticity solution in the limit of vanishingly small characteristic length is indicated for a particular type of boundary conditions. The solution for a circular inhomogeneity in an infinitely extended matrix subjected to remote shear stress is then derived. The effects of the imposed interface conditions, the shear stress and couple stress discontinuities, and the relationship between the inhomogeneity and its equivalent eigenstrain inclusion problem are discussed.